Privacy-preserving cryptocurrency exchanges (shielded AMMs, batched swap auctions, sealed-bid order-flow auctions) alter what the pricing mechanism observes about order flow. We derive the unique linear Kyle equilibrium when a committed Bayesian market maker observes order flow perturbed by independent Gaussian privacy noise. The price-impact coefficient and informed-trader strategy both rescale by a single factor in the privacy parameter, and their product is invariant. A welfare decomposition then identifies a closed-form per-period transfer from the protocol's LP pool to traders -- the "privacy subsidy", the break-even fee any privacy-aggregated exchange must charge. The result is the single-period closed-form privacy-noise analog of Loss-Versus-Rebalancing (Milionis et al. 2022). The primary application is shielded AMMs with explicit additive-noise injection (e.g., differential privacy); related designs (batched swaps, sealed-bid auctions, oracle-pegged crossings) require separate frameworks that we leave to future work.

翻译：隐私保护的加密货币交易所（屏蔽自动做市商、批量互换拍卖、密封指令流拍卖）改变了定价机制对指令流的观测方式。我们推导出，当承诺贝叶斯做市商观测到被独立高斯隐私噪声扰动的指令流时，存在唯一的线性Kyle均衡。价格冲击系数与知情交易者策略均按隐私参数的单一因子重新缩放，且二者乘积保持不变。福利分解进一步识别出从协议流动性池到交易者的封闭式每期转移——即"隐私补贴"，这是任何隐私聚合交易所必须收取的盈亏平衡费用。该结果是单期封闭式隐私噪声版本的损失-再平衡类比（Milionis等人，2022年）。主要应用场景为具有显式加性噪声注入（如差分隐私）的屏蔽自动做市商；而相关设计（批量互换、密封拍卖、预言机锚定交叉）则需要单独处理框架，我们将此留待未来研究。